Learning in Games with Unstable Equilibria

E. Hopkins, M. Benaim, J. Hofbauer

Research output: Contribution to journalArticlepeer-review


We propose a new concept for the analysis of games, the TASP, which gives a precise prediction about non-equilibrium play in games whose Nash equilibria are mixed and are unstable under fictitious play-like learning. We show that, when players learn using weighted stochastic fictitious play and so place greater weight on recent experience, the time average of play often converges in these "unstable" games, even while mixed strategies and beliefs continue to cycle. This time average, the TASP, is related to the cycle identified by Shapley [L.S. Shapley, Some topics in two person games, in: M. Dresher, et al. (Eds.), Advances in Game Theory, Princeton University Press, Princeton, 1964]. The TASP can be close to or quite distinct from Nash equilibrium.
Original languageEnglish
Pages (from-to)1694-1709
JournalJournal of Economic Theory
Issue number4
Publication statusPublished - Jul 2009


  • Games
  • Learning
  • Best response dynamics
  • Stochastic fictitious play
  • Mixed strategy equilibria;
  • TASP


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